Coarsening in one dimension: invariant and asymptotic states

Emanuel A. Lazar, Robin Pemantle

Research output: Contribution to journalArticlepeer-review


We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, then the average cell size grows at a prescribed exponential rate and the Poisson distribution is precisely invariant for the distribution of the whole process, rescaled in space by its average growth rate. We present numerical evidence toward the following universality conjecture: starting from any finite mean stationary renewal process, the system when rescaled by e−2t converges to a Poisson point process. For a limited case, this makes precise what has been observed previously in experiments and simulations, and lays the foundation for a theory of universal asymptotic states of dynamical cell complexes.

Original languageEnglish
Pages (from-to)59-84
Number of pages26
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Sep 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, Hebrew University of Jerusalem.


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